Scala analysis: xen15-gilson-didymus-diatonic
Didymus' Diatonic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 3/2 701.955 cents perfect fifth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 294.1 498.0 702.0 813.7 996.1 1200.0 111.7 : 182.4 386.3 590.2 702.0 884.4 1088.3 1200.0 294.1 : 203.9 407.8 519.6 702.0 905.9 1017.6 1200.0 498.0 : 203.9 315.6 498.0 702.0 813.7 996.1 1200.0 702.0 : 111.7 294.1 498.0 609.8 792.2 996.1 1200.0 813.7 : 182.4 386.3 498.0 680.4 884.4 1088.3 1200.0 996.1 : 203.9 315.6 498.0 702.0 905.9 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 167.47806 cents, oct.: 1172.34639 cents Scale is strictly proper Step pattern alph. order: ABCCABC Step pattern size order : SMLLSML Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.415885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.503263 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale is Hypolydian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 113.6850 cents: 5 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.043353 Average absolute harmonicity : 0.264856 Specific harmonicity : 0.245398 Fundamental : 1/270, -8.0768 octaves, 0.9690 Hz. Guide tone : 96, 6.5850 octaves, 25116.054 Hz. Exponens Consonantiae : 2.592000E+04, 14.66178 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 71.5, average 10.21429 Mersenne's string divisions : 12482925 Sum of van Prooijen's expressibility: 5.21491, average 0.74499 Sum of Tenney's harmonic distance : 11.23551, average 1.60507 Vogel's harmonic complexity : 13.57143 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 89.22730, average 3.18669 Lattice compactness (without 2's) : 47.94155, average 1.71220 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 2.57143 20 1 3: -3 .. 1 -0.85714 8 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 36.6619 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 33.4609 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 28.3980 c. M: 54.1350 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 34.4531 c. M: 50.0499 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 7.3898 c. M: 13.6863 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 29: 3 4 5 5 3 4 5 SP SD: 7.3735 c. M:-13.8999 c. 31: 3 5 5 5 3 5 5 SP M DE S SD: 7.7696 c. M:-15.5424 c. Intense Diatonic Dorian, M.Phrygian 34: 3 5 6 6 3 5 6 P SD: 6.2021 c. M: 11.7821 c. 41: 4 6 7 7 4 6 7 SP SD: 3.0704 c. M:-5.8259 c. 53: 5 8 9 9 5 8 9 SP SD: 0.7775 c. M:-1.4763 c. 65: 6 10 11 11 6 10 11 SP SD: 0.8806 c. M: 1.3786 c. 118: 11 18 20 20 11 18 20 SP SD: 0.3870 c. M:-0.7803 c. 171: 16 26 29 29 16 26 29 SP SD: 0.3831 c. M:-0.6018 c. 289: 27 44 49 49 27 44 49 SP SD: 0.3638 c. M:-0.6747 c. 323: 30 49 55 55 30 49 55 SP SD: 0.3286 c. M: 0.6365 c. 376: 35 57 64 64 35 57 64 SP SD: 0.2587 c. M: 0.5180 c. 388: 36 59 66 66 36 59 66 SP SD: 0.2405 c. M: 0.3911 c. 441: 41 67 75 75 41 67 75 SP SD: 0.1438 c. M: 0.2574 c. 494: 46 75 84 84 46 75 84 SP SD: 0.1058 c. M: 0.2079 c. 547: 51 83 93 93 51 83 93 SP SD: 0.1271 c. M:-0.2077 c. 559: 52 85 95 95 52 85 95 SP SD: 0.0552 c. M: 0.1034 c. 612: 57 93 104 104 57 93 104 SP SD: 0.0212 c. M:-0.0392 c. 1171: 109 178 199 199 109 178 199 SP SD: 0.0199 c. M: 0.0319 c. 1783: 166 271 303 303 166 271 303 SP SD: 0.0122 c. M: 0.0239 c. 2395: 223 364 407 407 223 364 407 SP SD: 0.0114 c. M: 0.0223 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 17.9552 cents 6 x 7:8:9:10:11:12 S SD: 15.4344 cents 7 x 8:9 x 11:12:14 SD: 22.6851 cents 8 x 9:11:12:13:14:16 SD: 18.5909 cents 9:10:11:12 x 14:16:18 S SD: 16.8417 cents 10:11:12:13:15:16:18:20 SD: 10.7705 cents 12:13:14:16:18:19:21:24 SD: 7.1938 cents 15:16:18:20:23:24:27:30 SD: 6.9589 cents 16:17:19:21:24:26:28:32 SD: 6.7980 cents 18:19:21:24:27:29:32:36 SD: 4.9806 cents 26:28:31:35:39:42:46:52 SD: 4.5189 cents 27:29:32:36:41:43:48:54 SD: 3.6682 cents 28:30:33:37:42:45:50:56 SD: 3.2367 cents 32:34:38:43:48:51:57:64 SD: 2.4585 cents 42:45:50:56:63:67:75:84 SD: 2.0456 cents 48:51:57:64:72:77:85:96 SD: 1.5876 cents 60:64:71:80:90:96:107:120 SD: 0.8632 cents 90:96:107:120:135:144:160:180 SD: 0.7717 cents 102:109:121:136:153:163:181:204 SD: 0.7463 cents 108:115:128:144:162:173:192:216 SD: 0.5163 cents 150:160:178:200:225:240:267:300 SD: 0.4369 cents 162:173:192:216:243:259:288:324 SD: 0.3439 cents 210:224:249:280:315:336:373:420 SD: 0.2470 cents 270:288:320:360:405:432:480:540 S SD: 0.0000 cents